Rig is moving other parts of my mesh for no reason!
In Object mode apply the rotation and scale of your object with ctrlA, then in Edit mode recalculate the normals with ctrlN.

Also maybe remove the doubles, put the Armature modifier above the Subsurf, enable the Preserve Volume of the Armature modifier, join the fingers to the hands, etc...

Anyway it will need some corrections in Weight Paint mode or with the Vertex Groups Assign button.